On Sep 22, 2010, at 8:02 , Brad Kemper wrote:
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> On Sep 21, 2010, at 4:21 PM, David Singer wrote:
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>> On Sep 21, 2010, at 11:21 , Brad Kemper wrote:
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>>>> And there is a long tradition in mathematics of the positive Y axis going up. But in HTML the Y axis goes down, because of the (western) tradition of reading from top to bottom.
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>>> I don't see how that is relevant to traditions of angle-based linear directions. You can still have 0deg=left-to-right and 90deg=bottom-to-top when y++ progresses downward. .
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>> whoa, the normal expectation is that 0 is the x-axis and that increasing angles move towards the positive Y-axis at 90 degrees (or the appropriate number of radians :-)).
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> That may be ingrained into your understanding of rotation, but I do not think it is a common way to think of angles as specifiers of linear direction. If someone asks me to draw a 45 degree angle, I draw a line pointing to the right and another line, connected to the first on the left, pointing up and to the right. If superimposed on a square it would go from lower left to upper right corners. When I draw that angle, it never enters my mind which direction the positive y-axis points, and I have no expectation that it matters. I really don't think I am unusual in thinking this way, except perhaps amongst a this crowd.
OK, but that's not quite what the question is. "Draw a line at 45 degrees" is more like it, and is likely to result in one of 3 responses:
a) 45 degrees to what?
b) given a piece of paper, a line from top left to bottom right
c) given a piece of paper, a line from bottom left to top right
I think many people, if asked, "on a cartesian grid, what is the relationship between a vector along the Y-axis and a vector at 90 degrees?" would say that they are the same, and surprise might not be enough if told that the Y axis is at MINUS 90 degrees. They may need astonishment.
David Singer
Multimedia and Software Standards, Apple Inc.